Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation
Abstract
An analytical model of the band gap narrowing (BGN) in silicon was derived from a non-self-consistent finite-temperature full random-phase approximation (RPA) formalism. Exchange-correlation self-energy of the free carriers and correlation energy of the carrier-dopant interaction were treated on an equal basis. The dispersive quasi-particle shift (QPS) in RPA quality was numerically calculated for a broad range of densities and temperatures. The dispersion was found to be smooth enough for the relevant energies to justify the rigid shift approximation in accordance with the non-self-consistent scheme. A pronounced temperature effect of the BGN only exists in the intermediate density range. The contribution of the ionic part of the QPS to the total BGN decreases from 1/3 at low densities to about 1/4 at very high densities. Based on the numerical results, Padé approximations in terms of carrier densities, doping, and temperature with an accuracy of 1 meV were constructed using limiting cases. The analytical expression for the ionic part had to be modified for device application to account for depletion zones. The model shows a reasonable agreement with certain photoluminescence data and good agreement with recently revised electrical measurements, in particular for p-type silicon. The change of BGN profiles in a bipolar transistor under increasing carrier injection is demonstrated.
- Publication:
-
Journal of Applied Physics
- Pub Date:
- October 1998
- DOI:
- 10.1063/1.368545
- Bibcode:
- 1998JAP....84.3684S
- Keywords:
-
- 85.30.De;
- 85.30.Pq;
- 71.20.Mq;
- 71.45.Gm;
- Semiconductor-device characterization design and modeling;
- Bipolar transistors;
- Elemental semiconductors;
- Exchange correlation dielectric and magnetic response functions plasmons